# Fits Proportional excess hazards model

### Description

Fits proportional excess hazards model.

The models are written using the survival modelling given in the survival package.

### Usage

1 2 | ```
prop.excess(formula=formula(data),data=sys.parent(),excess=1
,tol=0.0001,max.time=NULL,n.sim=1000,alpha=1,frac=1)
``` |

### Arguments

`formula` |
a formula object, with the response on the left of a ‘~’ operator, and the terms on the right. The response must be a survival object as returned by the ‘Surv’ function. |

`data` |
a data.frame with the variables. |

`excess` |
specifies for which of the subjects the excess term is present. Default is that the term is present for all subjects. |

`tol` |
tolerance for numerical procedure. |

`max.time` |
stopping considered time-period if different from 0. Estimates thus computed from [0,max.time] if max.time>0. Default is max of data. |

`n.sim` |
number of simulations in re-sampling. |

`alpha` |
tuning paramter in Newton-Raphson procedure. Value smaller than one may give more stable convergence. |

`frac` |
number between 0 and 1. Is used in supremum test where observed jump times t1, ..., tk is replaced by t1, ..., tl with l=round(frac*k). |

### Details

The program assumes that there are no ties, and if such are present random noise is added to break the ties.

### Value

Returns an object of type "prop.excess". With the following arguments:

`cum` |
estimated cumulative regression functions. First column contains the jump times, then follows the estimated components of additive part of model and finally the excess cumulative baseline. |

`var.cum` |
robust pointwise variance estimates for estimated cumulatives. |

`gamma` |
estimate of parametric components of model. |

`var.gamma` |
robust variance estimate for gamma. |

`pval` |
p-value of Kolmogorov-Smirnov test (variance weighted) for excess baseline and Aalen terms, H: B(t)=0. |

`pval.HW` |
p-value of supremum test (corresponding to Hall-Wellner band) for excess baseline and Aalen terms, H: B(t)=0. Reported in summary. |

`pval.CM` |
p-value of Cramer von Mises test for excess baseline and Aalen terms, H: B(t)=0. |

`quant` |
95 percent quantile in distribution of resampled Kolmogorov-Smirnov test statistics for excess baseline and Aalen terms. Used to construct 95 percent simulation band. |

`quant95HW` |
95 percent quantile in distribution of resampled supremum test statistics corresponding to Hall-Wellner band for excess baseline and Aalen terms. Used to construct 95 percent Hall-Wellner band. |

`simScoreProp` |
observed scoreprocess and 50 resampled scoreprocesses (under model). List with 51 elements. |

### Author(s)

Torben Martinussen

### References

Martinussen and Scheike, Dynamic Regression Models for Survival Data, Springer Verlag (2006).

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
###working on memory leak issue, 3/3-2015
###data(melanoma)
###lt<-log(melanoma$thick) # log-thickness
###excess<-(melanoma$thick>=210) # excess risk for thick tumors
###
#### Fits Proportional Excess hazards model
###fit<-prop.excess(Surv(days/365,status==1)~sex+ulc+cox(sex)+
### cox(ulc)+cox(lt),melanoma,excess=excess,n.sim=100)
###summary(fit)
###par(mfrow=c(2,3))
###plot(fit)
``` |

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